Download chapter 7 estimation of the line of sight depth of the

C HAPTER 7
E STIMATION OF THE L INE OF SIGHT
DEPTH OF THE S MALL M AGELLANIC
C LOUD USING THE R ED C LUMP STARS
7.1
Introduction
The studies of Mathewson et al. (1986) and Mathewson et al. (1988) found that the
SMC cepheids extend from 43 to 75 kpc with most cepheids found in the neighbourhood
of 59 kpc. Later, Welch et al. (1987) estimated the line of sight depth of the SMC by
investigating the line of sight distribution and period - luminosity relation of cepheids.
They accounted for various factors which could contribute to the larger depth estimated
by Mathewson et al. (1986) & Mathewson et al. (1988), and found the line of sight depth
of the SMC to be ∼ 3.3 kpc. Hatzidimitriou & Hawkins (1989), estimated the line of sight
depth in the outer regions of the SMC to be around 10-20 kpc.
In this study, we used the dispersions in the colour and magnitude distribution of RC stars
for depth estimation. The dispersion in colour is due to a combination of observational
error, internal reddening (reddening within the SMC) and population effects. The dispersion in magnitude is due to internal extinction, depth of the distribution, population
effects and photometric errors associated with the observations. By deconvolving other
effects from the dispersion of magnitude, we estimated the dispersion only due to the
depth of the SMC. The advantage of choosing RC stars as a proxy is that there are large
numbers of these stars available to determine the dispersions in their distributions with
good statistics, throughout the SMC. The depth of the intermediate age component of the
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7.2 Data & Analysis
SMC may give clues to the formation and evolution of the SMC, and thus in turn would
give clues to the interactions between the LMC and SMC.
7.2
Data & Analysis
The V and I band photometric data from the OGLE II and MCPS catalog are used for
this study. The OGLE II and the MCPS fields are divided into 176 sub-regions (each subregion having an area of 7.12×7.12 square arcmin), and 876 sub-regions (each having an
area of ∼ 8.9×10 square arcmin) respectively. The data in the central regions may suffer
from incompleteness due to crowding effects. The incompleteness in the OGLE II data
is corrected using the values given in Udalski et al. (2000). The effect of crowding in the
MCPS data is discussed in section 7.5. As explained in section 2.2.1, the RC stars are
identified from the (V − I) vs I CMD of each sub-region. Out of 876 sub-regions of the
MCPS field, only 755 regions have a reasonable number of RC stars to do the analysis.
The number of RC stars in each region depends on the stellar density. The number is large
in the central regions, whereas it decreases in the disk. The number of RC stars ranges
between 1000 - 3000 in the bar region, whereas the range is 100 - 1500 in the disk. For
both the data sets, only data with errors less than 0.15 mag are taken for the analysis.
As discussed in section 2.2.2 the width corresponding to the line of sight depth can
be obtained from the colour and magnitude distributions of the RC stars. To obtain the
number distribution of the RC stars in each region, the data are binned with a bin size
of 0.01 and 0.025 mag in colour and magnitude respectively. The width in colour and
magnitude distributions are obtained using non-linear least square fits. Along with the
width of the distributions, the error in the estimation of each parameter and the goodness
of the fit, which is the same as the reduced χ2 value are obtained. Regions with reduced χ2
values greater than 2.6 are omitted from the analysis. As the important parameter for our
calculations is the width associated with the two distributions, we also omitted regions
with fit error of width greater than 0.1 mag from our analysis. After these omissions,
the number of regions useful for analysis in OGLE II and MCPS data sets are 150 and
600 respectively. Thus, the total observed dispersion in (V−I) colour and I magnitude are
estimated for the RC stars in all these regions.
From the observed dispersions in the colour and magnitude distributions of the RC
stars, width corresponding to the line of sight depth and the error associated with it are
obatined. The relations used are given in section 2.2.2. To convert the internal reddening
to internal extinction we used the Rieke & Lebofsky (1985) interstellar extinction relation
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7.3 Internal reddening in the SMC
of our Galaxy. The relation is given by AI = 0.934 x E(V − I). The interstellar extinction
law of our Galaxy is adopted for the calculations of Magellanic Clouds based on the
results of the studies by Nandy & Morgan (1978), Lequeux et al. (1982) and Misselt et al.
(1999), which showed that the SMC has extinction curve similar to that found in our
Galaxy. The error associated with the line of sight depth will translate as the minimum
depth that can be estimated. The minimal depth that can be estimated is ∼ 350 pc in the
central regions and ∼ 670 pc in the outer regions.
7.3
Internal reddening in the SMC
One of the by product of this study is the estimation of internal reddening in the SMC.
In this study, we used the width of the (V−I) colour distribution to estimate the internal
reddening map across the MCs. This estimates the front to back reddening of a given
region in the SMC, which we call as the internal reddening (in E(V−I)), and does not
estimate the reddening between the front end of the region and the observer. Thus, this
estimate traces the reddening within the SMC and hence the location of the dust. The
estimates and figures given below thus gives the internal reddening within the SMC.
The colour coded figure of the internal reddening in the SMC is presented in Fig. 7.1.
It can be seen that the internal reddening is high only in some specific regions. Most of
the regions have very negligible internal reddening suggesting that most of the regions in
the SMC are optically thin. A region of high internal reddening is found to the west of
the optical center. Also, the bar region is found to have some internal reddening, whereas
the outer regions have very little internal reddening (within the area studied). The highest
reddening estimated is E(V−I) = 0.08 mag in the OGLE II regions and 0.12 mag in the
MCPS region. These regions are located close to the optical center. The rest of regions
have very little internal reddening. Thus, our results indicate small internal extinction
across the SMC, as seen by the RC stars. The minimum internal reddening that can be
estimated is 0.002 mag in the central regions and 0.005 mag in the outer regions.
7.4
Results
We used OGLE II and MCPS data sets for this study. The area covered by OGLE II
is mainly the bar region, whereas the bar and the surrounding regions are covered by the
MCPS data.The depth of 150 regions (OGLE II data) and 600 regions (MCPS data) of
the SMC were calculated.
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7.4 Results
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Min internal reddening
E(V-I)<0.01
0.01<E(V-I)<0.03
0.03<E(V-I)<0.05
0.05<E(V-I)<0.07
0.07<E(V-I)<0.09
E(V-I)>0.09
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Figure 7.1: Two dimensional plot of the internal reddening in the SMC. The colour code
is given in the figure. The magenta dot represents the optical center of the SMC. The
upper plot is derived from the MCPS data, whereas the lower plot is derived from the
OGLE II data.
A colour coded, two dimensional plot of depth for these two data sets are shown in
Fig. 7.2. OGLE II data is shown in the lower panel and MCPS data in the upper panel.
The optical center of the SMC is taken to be R.A = 00h 52m 12.5 s , Dec = -720 49’ 43”
(J2000, de Vaucouleurs & Freeman 1972). There is no indication of a variation of depth
across the SMC as indicated by the uniform distribution of the red and black dots. The
prominent feature in both the plots is the presence of blue and green points indicating
increased depth, for regions located near the SMC optical center. The OGLE II data
cover only the bar region and it can be seen that this data is not adequate to identify the
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extension of the central feature, whereas the MCPS data clearly delineates this feature.
The net dispersions range from 0.10 to 0.35 mag (a depth of 2.8 kpc to 9.6 kpc) in
the OGLE II data set and from 0.025 mag to 0.34 mag (a depth of 670 pc to 9.47 kpc)
in the MCPS data set. The minimum depth estimated in the MCPS data is limited by
errors. The fraction of such regions where the minimum value is limited by errors is
2.83%. The average value of the SMC thickness estimated using the OGLE II data set in
the central bar region is 4.9± 1.2 kpc and the average thickness estimated using MCPS
data set, which covers a larger area than OGLE II data, is 4.42 ± 1.46 kpc. The average
depth obtained for the bar region alone is 4.97 ±1.28 kpc, which is very similar to the
value obtained from OGLE II data. The depth estimated for the region excluding the bar
is 4.23±1.47 kpc. Thus the bar and the surrouning regions of the SMC do not show any
significant difference in the depth. The marginal difference in the depth values between
the bar and the surrounding regions is due to the presence of higher depth regions near the
center. Thus, except for the central feature, the depth across the SMC appears uniform.
Our estimate is in good agreement with the depth estimate of the SMC using eclipsing
binary stars by North et al. (2009). They estimated a 2-sigma depth of 10.6 kpc, which
corresponds to a 1-sigma depth of 5.3 kpc.
In order to study the variation of depth of the SMC (OGLE II data) along the R.A,
dispersion corresponding to the depth is plotted against R.A in Fig. 7.3. The lower panel
shows all the regions along with the error in depth estimation for each location. The upper
panel shows the depth averaged along Dec and the error indicates the standard deviation
of the average. Both the panels clearly show the increased depth near the SMC center.
There is no significant variation of depth along the bar.
For the MCPS data, the dispersion corresponding to depth is plotted against R.A as
well as DEC in figure 7.4. There is an indication of increased depth near the center. The
plot also indicates that there is no significant variation in depth between the bar and the
surrounding regions. In Fig. 7.5, the depth averaged over R.A and Dec are shown in the
upper and lower panel respectively. These are plotted for a small range of Dec (-72.0 to
-73.8 degrees) and R.A (10 - 15 degrees), in order to identify the increased depth in the
central region.The increased depth near the center is clearly indicated. Thus, the depth
near the center is about 9.6 kpc, which is twice the average depth of the bar region (4.9
kpc). Thus, the SMC has a more or less uniform depth of 4.9 ±1.2kpc over bar as well as
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Min depth
Min depth<t<2.0Kpc
2.0Kpc < t < 4.0Kpc
4.0Kpc < t < 6.0Kpc
6.0Kpc < t < 8.0Kpc
8.0Kpc < t < 10.0Kpc
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Figure 7.2: Two dimensional plot of depth (t) in the SMC. Upper panel is for the MCPS
data and lower panel is for OGLE II data.The colour code is same for both the panels.
The magenta dot represents the optical center of the SMC. The empty squares represent
the omitted regions with poor fit.
Table 7.1: Depths of different regions in the SMC. These are line of sight depths and need
to be corrected for inclination, to estimate the actual depth.
Region
SMC bar
SMC region excluding the bar
Range of depth (kpc)
Avg.depth (kpc)
Std.deviation (kpc)
3.07-9.53
0.67-9.16
4.90
4.23
1.23
1.48
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7.5 Discussion
OGLE DATA
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Figure 7.3: Lower panel: Width corresponding to depth against R.A for bar region of the
SMC (OGLE II data). Upper panel: Average of depth along the declination against R.A
in the bar region of the SMC (OGLE II data).
the surrounding regions, with double the depth near the center.
7.5
Discussion
As incompleteness correction is done in one data set (OGLE II) and not in the other
(MCPS), we compared the depth estimates before and after adopting the completeness
correction. We found that the change is within the bin sizes adopted here. Thus, incorporating the incompleteness correction has not changed the results presented here. The
incompleteness correction in the central regions is about 12% and that in the outer region
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7.5 Discussion
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Figure 7.4: Width corresponding to depth against R.A in the lower panel and against Dec
in the upper panel for the SMC (MCPS data).
is about 5%. The incompleteness in the MCPS data does not affect the results presented
here.
We have removed regions in the MCs with poor fit as explained in section 7.2. These
regions are likely to have different RC structures suggesting a large variation in metallicity
and/or population. The fraction of such region is about 5.3%. Such regions are indicated
in Fig. 7.2. Thus to a certain extent, the above procedure has eliminated the regions with
very different metallicity and star formation history that are seen in most of the regions.
Apart from the above, the remaining regions studied here might have some variation in
the the RC population contributing to the depth estimated. The results presented in this
study will include some contribution from the population effect.
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7.5 Discussion
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Figure 7.5: Lower panel: Width corresponding to depth averaged over Dec and plottedagainst R.A for a small range of Dec in the central region of the SMC (MCPS data). Upper
panel: Width corresponding to depth averaged over R.A and plotted against Dec for a
small range of R.A in the central region of the SMC (MCPS data).
For the estimation of the internal extinction from internal reddening we used the relation, AI = 0.934 x E(V − I) (Rieke & Lebofsky 1985). As explained in section 3.5 ,the
above interstellar extinction relation is appropriate for the broad Johnson I filter and the
appropriate conversion factor between AI and E(V − I) for OGLE and MCPS bands is ∼
1.4. In order to check the effect of the choice of this conversion factor in our results, we
repeated the whole analysis using the relation AI = 1.4 x E(V − I). From this analysis
we obtained mean values of 4.90 ± 1.24 kpc and 4.23 ± 1.47 kpc for the bar and for the
regions excluding the bar respectively. These values are very similar to those given in
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Figure 7.6: Two dimensional plot of density distribution estimated from MCPS data. The
small open circles in the central region indicate the high density regions. The ellipse
shows the boundary of regions with large depth, the large hexagons indicate the stellar
peaks found by Cioni et al. (2000a), the large triangle indicate the HI peak (Stanimirović
et al. 2004) and the large square denotes the optical center.
table 7.1. This suggests that the choice of E(V − I) to AI conversion factor has not much
effect in our present analysis. This may be due to the the low values of internal reddening
as seen from the Fig. 7.1.
The SMC is found to have a depth greater than the LMC. The bar and the surrounding
regions do not show much difference in depth. The profile of the depth near the center
(Fig. 7.5) looks very similar to a typical luminosity profile of a bulge. This could suggest
the presence of a bulge near the optical center of the SMC. If a bulge is present, then a
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density/luminosity enhancement in this region is also expected. We plotted the observed
stellar density in each region from the MCPS data to see whether there is any such central
enhancement. This is shown in Fig. 7.6. The regions with high density are shown as
open circles, located close to the optical center. The regions with large depth are found to
be within the ellipse shown in the figure. It can be seen that regions with highest stellar
density lie more or less within this ellipse. Cioni et al. (2000a) studied the morphology
of the SMC using the DENIS catalogue. They found that the distribution of AGB and
RGB stars show two central concentrations, near the optical center, which match with the
carbon stars by Hardy et al. (1989). They also found that the western concentration is
dominated by old stars. The approximate locations of these two concentrations found by
Cioni et al. (2000a) are shown as hexagons in Fig. 7.6. Also, the strongest H I concentration in the SMC map by Stanimirovic et al. (1999) falls between these two concentrations.
The maximum H I column density, 1.43 × 1022 atoms cm−2 is located at R.A = 00h 47m
33 s , Dec = -730 05’ 26” (J2000.0) (Stanimirović et al. 2004). This location is shown as
a large triangle in Fig. 7.6. The optical center of the SMC is shown as a large square.
All these peaks as well as the optical center are located on or within the boundary of the
ellipse. Thus, the peaks of stellar as well as the H I are found within the central region
with large depth. This supports the idea that a bulge may be present in the central SMC.
This bulge is not very luminous, but clearly shows enhanced density. It is also the central
region of the triangular shaped bar.
The increased dispersion near the SMC center, which is interpreted as due to large
depth, could be partially due to the presence of RC population which is different. Cioni
et al. (2006b) did not find any different population or metallcity gradient near the central
regions. Tosi et al. (2008) obtained deep CMDs of 6 SMC regions to study the star
formation history. Three of their regions are located close to the bar and three are outside
the bar. They found an apparent homogeinty of the old stellar population populating the
subgiant branch and the clump. This suggested that there is no large differences in age
and metallicity among old stars in these locations. Their SF1 region is located close to
the region of large depth identified here. The RC population in this region is found to
be very rich and the spread in magnitude is greater than those found in the other CMDs.
This spread is also suggestive of increased depth near this location. It will be worthwhile
to study the star formation history of regions near the SMC center to understand how
different the stellar population is in this suggested bulge.
It may be worthwhile to see whether this bar is actually an extended/deformed bulge.
It is interesting that the so-called triangular shaped bar of the SMC is also an unexplained
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7.6 Conclusions
component, which does not show the signatures of a typical bar. This could naturally
explain the formation of the odd shaped bar in the SMC. Thus, we propose that the central
SMC has a bulge. The elongation and the rather non-spherical appearance of the bulge
could be due to tidal effects or minor mergers (Bekki & Chiba 2008).
7.6
Conclusions
• The SMC bar and the disk have similar depth, with no significant depth variation
across the disk. The estimated depth for the bar and the disk regions are 4.9±1.23 kpc
and 4.23±1.48 kpc respectively.
• Increased depth (∼ 8-10 kpc) is found near the optical center of the SMC.
• The increased depth and the enhancement in the stellar & H I density near the
center, suggest that the SMC possibly has a bulge. The central bar may be this deformed/extended bulge.
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